Pakistan's army does not believe the Pakistani Taliban were behind the Times Square bomb attempt as the insurgent group has claimed, a spokesman said Wednesday.

The renewed casting of doubt over the Taliban's claim comes as militants again insist their fundamentalist movement was behind the propane-filled SUV, showing a clear public relations battle that the Obama administration must now wade through for both security and political reasons.

In a video message on Sunday, the group said it carried out the attack, in what would be the first time it had been known to strike outside South Asia.

Speaking to CBS News' Sami Yousafzai Wednesday, a Taliban source called the plot "pure Pakistani Taliban," claiming the militants were "involved A to Z" in the planning and execution.

U.S. officials quickly dismissed the initial claim, but the arrest of Faisal Shahzad, a Pakistani-American who allegedly has admitted to being trained in the group's heartland in Waziristan has given it new credence.

Maj. Gen. Athar Abbas, the military's chief spokesman, said the claim should be "taken with a pinch of salt."

"Anybody can claim anything, but whether the organization has that kind of reach is questionable. I don't think they have the capacity to reach the next level," he said.

The attack is likely to increase pressure on the Pakistani army to launch a new offensive in the northern part of Waziristan, something it has been avoiding until now. U.S. and European officials have long said that many of the terror plots in the West are hatched in the region.

Shahzad only became a naturalized U.S. citizen last year. CBS News correspondent Mandy Clark reports that he recently returned from an eight-month trip to his homeland.

A Pakistani intelligence officer has told CBS News that Shahzad spent four to five months in Peshawar, in the country's North West Frontier Province, but was born in the Punjab in Eastern Pakistan.

Abbas declined to comment on reports that the suspect had been to Waziristan for training.

The way the Taliban movement made its claim of responsibility for Shahzad's alleged plot, and the failed execution of the bombing also raise questions over the level of the militant group's involvement.

CBS News' Khaled Wassef who monitor's online jihadi propaganda, says the initial claim of responsibility came just a day after the failed attack in the form of a video statement from Taliban spokesman Qari Hussain. It was short, and it was posted on Youtube rather than the usual jihadi blogs or on the Taliban's own website.

It was also very vague, claiming responsibility for the "recent attack in the U.S.A.". It does not mention New York specifically, nor the type of bomb that was used.

CBS News justice correspondent Bob Orr noted Tuesday that it would be unusual for a well-developed international plot to involve one perpetrator who obtains the materials, builds the device, positions it and then carries out the attack all on his or her own.

However, former Deputy Assistant FBI Director Harry "Skip" Brandon tells CBS' "The Early Show" Shahzad may actually represent a shift in tactic by militant groups to more lone-wolf style attacks. Brandon said Shazhad may be an "unguided missile," given some training by the Taliban but then essentially unleashed and just told to "go do something".

The Pakistani army had claimed to have delivered the Pakistani Taliban a decisive blow in an operation late last year in South Waziristan. But the notion that the Pakistani Taliban are on the ropes has been shaken by the emergence of videos of a top commander previously believed to have been killed, and the group's claims of responsibility for the Times Square bomb attempt.

Shahzad's links to the group may not be much deeper than him reaching out to the Taliban and then receiving some weapons training. And their explosives training clearly didn't work as well as hoped - the device in the SUV was made using fertilizer that was unlikely to blow up and propane canisters that are carefully designed not to blow up.

But the Pakistani government's continued denial that the Taliban is capable of reaching out, all the way to U.S. soil, is being tested by mounting evidence that Shazhad did, in fact, spend time training at one of their camps.

Mandy Clark reports that Pakistani police have arrested at least two people in Karachi in connection to the case. One of them, Tauseef Ahmed, is believed to have traveled to the U.S. two months ago to meet with Shahzad.

CBS News has also learned that Shahzad may have spent at least four months training at a terrorist camp affiliated with Pakistan's Taliban - raided in early March by Pakistani forces.

Pakistan's Interior Minister Rehman Malik tells CBS News that Shehzad travelled 13 times to Pakistan between 2003 and his arrest. The only year he did not return home was 2006. Most of his entries on trips back to Pakistan were via Islamabad or Peshawar.

Somewhere between the Taliban's claim of "A to Z" responsibility, and the Pakistani authorities' eagerness to disassociate their domestic terror groups from attempted attacks in the U.S. - a key ally and source of economic aid - likely lies the truth.

Finding that truth is the task of the American intelligence agencies. Figuring out how to deal with it is President Obama's next challenge in the delicate political-military balancing act with the country still on the frontline of the war against extremism, whether they like to admit it or not.